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Centre of mass of solid cone

  1. Mar 29, 2015 #1
    1. The problem statement, all variables and given/known data

    Find the centre of mass of solid cone.
    2. Relevant equations

    $$y_{cm}=\frac{1}{M}\int_0^Hydm$$
    3. The attempt at a solution
    First I took thin disks. I got the answer when I assumed its thickness to be dy but then dysecθ would be more accurate if half angle of cone is θ since dysecθ gives the length of the slanted part, while dy would give a cylinder.
    20150329_112303-1.jpg
    Now I get wrong answer.
     

    Attached Files:

  2. jcsd
  3. Mar 29, 2015 #2

    ehild

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    But the volume of a truncated cone is (h pi/3 )(r12+r1r2+r22) where r1 and r2 are the radii of the base plates and h is the height. In case of the volume element, r1≈r2=r and h=dy, so the volume element is that of a disk with radius r and height dy.

    Also, you have to use density times Ady instead of dm in the integral.
     
    Last edited: Mar 29, 2015
  4. Mar 29, 2015 #3
    OK. But whats wrong in dysecθ?
     
  5. Mar 29, 2015 #4

    ehild

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    Nothing is wrong with it if you do not use it instead of dy.
     
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